Guides / Maths

How to Calculate Percentages: Three Common Cases

Almost every percentage question is one of three types. Once you can spot which one you have, the calculation is short.

1. What is X% of Y?

Turn the percentage into a decimal by dividing by 100, then multiply.

Example: 15% of 200 = 0.15 × 200 = 30.

This is the case for tips, discounts and sales tax.

2. X is what percent of Y?

Divide the part by the whole, then multiply by 100.

Example: 45 out of 180 is 45 ÷ 180 × 100 = 25%.

Use this for test scores, survey results and budget shares.

3. Percentage change from X to Y

Subtract the starting value from the new one, divide by the starting value, then multiply by 100. A positive result is an increase and a negative one is a decrease.

Example: from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%.

Always divide by the starting value, not the new one. Going from 100 to 80 is a 20% drop, but going from 80 to 100 is a 25% rise.

Quick checks

• 10% is the same as moving the decimal point one place left.
• A 50% increase and a 50% decrease do not cancel out. 100 up 50% is 150, and 150 down 50% is 75.

Try it yourself

The Percentage Calculator answers all three questions as you type.